| dc.contributor.advisor | 陳天進 | zh_TW |
| dc.contributor.advisor | Chen, Ten Ging | en_US |
| dc.contributor.author (Authors) | 歐姿君 | zh_TW |
| dc.contributor.author (Authors) | Ou, Tze Chun | en_US |
| dc.creator (作者) | 歐姿君 | zh_TW |
| dc.creator (作者) | Ou, Tze Chun | en_US |
| dc.date (日期) | 2007 | en_US |
| dc.date.accessioned | 17-Sep-2009 13:48:01 (UTC+8) | - |
| dc.date.available | 17-Sep-2009 13:48:01 (UTC+8) | - |
| dc.date.issued (上傳時間) | 17-Sep-2009 13:48:01 (UTC+8) | - |
| dc.identifier (Other Identifiers) | G0094751008 | en_US |
| dc.identifier.uri (URI) | https://nccur.lib.nccu.edu.tw/handle/140.119/32586 | - |
| dc.description (描述) | 碩士 | zh_TW |
| dc.description (描述) | 國立政治大學 | zh_TW |
| dc.description (描述) | 應用數學研究所 | zh_TW |
| dc.description (描述) | 94751008 | zh_TW |
| dc.description (描述) | 96 | zh_TW |
| dc.description.abstract (摘要) | Haymen猜測:對任意的超越半純函數 f(z)，f`(z)f(z)^n 取所有值無窮多次，其中至多只有一個例外值。這個著名的猜測，大部分的情形已被證明是正確的。另外，Hayman 證明 f`(z)-af(z)^n 取所有有限值無窮多次，其中 a 為一複數且 n≧5 的正整數。在本篇論文裡，我們將探討以小函數為係數的半純函數微分多項式之值分佈問題。並將Hayman的結果推廣至 f^{k}(z)f(z)^n 與 f^{k}(z)-af(z)^n 的情形。同時，我們也證明一些A類半純函數與其導數的值分佈結果。 | zh_TW |
| dc.description.abstract (摘要) | A famous conjecture of Hayman says that if f(z) is a transcendental meromorphic function, then f`(z)f(z)^n assumes all finite values except possibly zero infinitely often. The conjecture was solved in most cases. Another result of Hayman says that f`(z)-af(z)^n, where n≧5 and a is a complex number, assumes all finite values infinitely often. In this thesis, we will study the value distribution of some differential polynomial in a meromorphic function with small functions as coefficents. In fact, we will generalize Hayman`s results to the cases f^(k)(z)f(z)^n and f^(k)(z)-af(z)^n. Also, the value distribution of meromorphic functions of class A with their derivatives are obtained. | en_US |
| dc.description.tableofcontents | 謝辭......................................................i Abstract................................................iii 中文摘要..................................................iv 1 Introduction............................................1 2 Basic Theory of Nevanlinna`s Value Distribution Theory......................4 3.Some Lemmas.............................14 4.Value Distribution of Meromorphic Functions in class A with Their Derivatives..............16 5.Value Distribution of Meromorphic Functions with Their Derivatives...............................21 6.References.............................................................33 | zh_TW |
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| dc.language.iso | en_US | - |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#G0094751008 | en_US |
| dc.subject (關鍵詞) | 值分佈理論 | zh_TW |
| dc.subject (關鍵詞) | 半純函數 | zh_TW |
| dc.subject (關鍵詞) | value distribution theory | en_US |
| dc.subject (關鍵詞) | meromorphic function | en_US |
| dc.title (題名) | 半純函數與其導數之值分佈 | zh_TW |
| dc.title (題名) | On The Value Distribution Of Meromorphic Functions With Their Derivatives | en_US |
| dc.type (資料類型) | thesis | en |
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